The Conservatives lost their majority after UKIP rearranged the political landscape by winning 16 seats at last week’s county elections.
The result saw the Conservatives returned to County Hall with just 36 seats – and UKIP the next biggest party.
Labour has 12 seats, the Lincolnshire Independents eight, Liberal Democrats three and there are two Independents.
Conservative Coun Hill said: “I’m delighted that we have been able to reach this agreement. This will give us a firm foundation for the next four years, so the council can continue to focus on the issues that matter most to local people. I look forward to working alongside my new colleagues. I’m sure that together we can achieve things that benefit all our local communities.”
No further details are avaialble at present.